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Asymptotic distributions for downtimes of monotone systems

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

J. Gåsemyr  and
Terje Aven
J. Gåsemyr*
Affiliation:
University of Oslo
Terje Aven*
Affiliation:
Stavanger University College and University of Oslo
*
∗Postal address: University of Oslo, Department of Mathematics, P.O. Box 1053, Blindern, 0316 Oslo, Norway.
∗∗Postal address: Stavanger University College, Ullandhaug, 4091 Stavanger, Norway.
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Abstract

Consider a monotone system with independent alternating renewal processes as component processes, and assume the component uptimes are exponentially distributed. In this paper we study the asymptotic properties of the distribution of the rth downtime of the system, as the failure rates of the components converge to zero. We show that this distribution converges, and the limiting function has a simple form. Thus we have established an easy computable approximation formula for the downtime distribution of the system for highly available systems. We also show that the steady state downtime distribution, i.e. the downtime distribution of a system failure occurring after an infinite run-in period, converges to the same limiting function as the failure rates converge to zero.

Keywords

Downtime distributionmonotone systemsalternating renewal process

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 814 - 824
Copyright
Copyright © Applied Probability Trust 1999 

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